Hi Iuliana,
Yes, it is possible that this could happen, if the coronal mass ejection is strong enough. This is one of the reasons why there are many scientists working on the problems of (a) how to predict and understand coronal mass ejections, and (b) how to protect power and communications systems from the effect. Exactly how big an ejection should be to have drastic consequences is not exactly known. But here's a nice article about how scientists try to figure out the consequences of a large coronal mass ejection hitting the Earth:
http://www.space.com/2180...-grids-research.html